# OADR Marginal Effects and Interpretation

Sample mean OADR = 0.125 (12.5%).
OADR is measured as a fraction (0.10 = 10%). Coefficients refer to unit changes in this fraction.

## Model Coefficients

| Dependent Variable | OADR (linear) | SE | p-value | OADR² | SE | p-value | N |
|:--|--:|--:|--:|--:|--:|--:|--:|
| Expenditure/GDP | 126.3*** | 19.0 | 0.0000 | -155.5*** | 51.1 | 0.0024 | 3,776 |
| Revenue/GDP | 38.2* | 20.1 | 0.0578 | 19.5 | 53.7 | 0.7160 | 3,787 |
| Fiscal Gap | 55.5*** | 10.3 | 0.0000 | -123.4*** | 29.4 | 0.0000 | 3,776 |

## Marginal Effects at Representative OADR Levels

ME(OADR) = β_linear + 2 × β_quadratic × OADR

| OADR | Expenditure ME | Revenue ME | Fiscal Gap ME |
|:--|--:|--:|--:|
| 5% | 110.8 (±19.7) | 40.2 (±20.8) | 43.2 (±10.7) |
| 10% | 95.2 (±21.6) | 42.1 (±22.8) | 30.9 (±11.9) |
| 15% | 79.7 (±24.4) | 44.1 (±25.8) | 18.5 (±13.6) |
| 20% | 64.1 (±27.9) | 46.0 (±29.5) | 6.2 (±15.6) |
| 25% | 48.6 (±31.8) | 48.0 (±33.6) | -6.2 (±18.0) |
| 30% | 33.0 (±36.1) | 49.9 (±38.0) | -18.5 (±20.4) |

## Effect of 10pp OADR Increase (Integral of Marginal Effects)

| Transition | Expenditure (pp GDP) | Revenue (pp GDP) | Fiscal Gap (pp GDP) |
|:--|--:|--:|--:|
| 5% → 15% | +9.5 | +4.2 | +3.1 |
| 10% → 20% | +8.0 | +4.4 | +1.9 |
| 15% → 25% | +6.4 | +4.6 | +0.6 |
| 20% → 30% | +4.9 | +4.8 | -0.6 |

## Interpretation for Paper

At the sample mean OADR (12.5%), the marginal effect of a 1pp OADR increase is +0.87pp on expenditure/GDP and +0.43pp on revenue/GDP.

A 10pp OADR increase from 13% to 23% implies +7.2pp expenditure/GDP and +4.5pp revenue/GDP, opening a fiscal gap of 2.7pp of GDP.